and many more benefits!

Find us on Facebook

GMAT Club Timer Informer

Hi GMATClubber!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Re: The sum of prime numbers that are greater than 60 but less [#permalink]

Show Tags

23 Jul 2012, 09:55

5

This post receivedKUDOS

1

This post wasBOOKMARKED

B.) 128

I did this two ways.

The first way used a combination of pure processing power and logic. You know the even numbers - 62, 64, 66, and 68 will never be prime. 65 will always be divisible by 5. That leaves 61, 63, 67, and 69. 63 and 69 are divisible by 9 and 3 respectively (just plug and chug). That leaves you with 2 primes - 61 and 67 - the sum of which is 128.

The second way - applying divisibility rules - seems more elegant and more efficient in the long run:

For 2: All even numbers. This eliminates 62, 64, 66, and 68.For 3: Add up all the digits of the number. If the sum is divisible by 3, the number is divisible by 3. This eliminates both 63 and 69.For 4: If the last 2 digits of the number are divisible by 4, the entire number is divisible by 4. This does not apply to any of our remaining numbers - 61, 65, and 67. For 5: All numbers ending in 5 or 0. This eliminates 65, leaving only 61 and 67 in the running for primes. For 6: If the number is divisible by BOTH 2 & 3 (see first two rules), then the number is also divisible by 6. This does not apply to 61 and 67 since neither is divisible by 2 or 3. For 7: No concise rule that I know of. I recommend long-division or mental math. Does anyone know a quick way to check for divisibility by7? Regardless, you can run through the multiples of 7 and realize none fall on 61 or 67 so this divisor doesn't check out. For 8: If the last 3 digits are divisible by 8, then the whole number is divisible by 8. I didn't stick to this rule when using the divisibility rules approach. You know 2 is a prime factor of 8 meaning any number that has 8 as a multiple must be even. Since neither 61 nor 67 is even, 8 cannot be a divisor. For 9: Add up all the digits and see if the resulting sum is divisible by 9. This does not work when applied to 61 or 67 and is redundant for 63 (we knocked 63 out in the "For 3" rule).

Re: The sum of prime numbers that are greater than 60 but less [#permalink]

Show Tags

10 Oct 2013, 09:26

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Re: The sum of prime numbers that are greater than 60 but less [#permalink]

Show Tags

14 Nov 2015, 00:15

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Re: The sum of prime numbers that are greater than 60 but less [#permalink]

Show Tags

19 May 2016, 09:23

Bunuel wrote:

The sum of prime numbers that are greater than 60 but less than 70 is

(A) 67(B) 128(C) 191(D) 197(E) 260

A prime number is a number that has only two factors: 1 and itself. Therefore, a prime number is divisible by two numbers only.

Let's list the numbers from 61 to 69.

61, 62, 63, 64, 65, 66, 67, 68, 69

Immediately we can eliminate the EVEN NUMBERS because they are divisible by 2 and thus are not prime.

We are now left with: 61, 63, 65, 67, 69

We can next eliminate 65 because 65 is a multiple of 5.

We are now left with 61, 63, 67, 69.

To eliminate any remaining values, we would look at those that are multiples of 3. If you don’t know an easy way to do this, just start with a number that is an obvious multiple of 3, such as 60, and then keep adding 3.

We see that 60, 63, 66, 69 are all multiples of 3 and therefore are not prime.

Thus, we can eliminate 63 and 69 from the list because they are not prime.

Finally, we are left with 61 and 67, and we must determine whether they are divisible by 7. They are not, and therefore they must be both prime. Thus, the sum of 61 and 67 is 128.

Answer B.

Here is a useful rule: If a two-digit number is a prime, it can’t be divisible by any of the single-digit primes. That is, it can’t be divisible by 2, 3, 5 and 7. In other words, if you have a two-digit number that is not divisible by 2, 3, 5 and 7, it must be a prime. If you have trouble seeing that 61 and 67 are prime, I would suggest that you review your multiplication tables. Doing so will allow you to quickly see that 61 and 67 are not multiples of a given single-digit number, such as 7.
_________________